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Math 211 Multivariable Calculus Syllabus

The official syllabus in printable pdf form. Updated 29 August 2011.

The text Calculus: Multivariable, 5th ed will be referred to as CM.

Weekly Syllabus

  1. Thu 25 Aug
    Introduction (history of single variable, history of multivariable calculus), vectors, review of single variable calculus space (1-, 2-, 3-dimensional), describing curves by equations (implicitly) and by parameterization. CM 12.1,2,5.

  2. Tue 30 Aug
    Moving between implicit and parameterized descriptions, multivariable functions (single variable R -> R, parametrized curves R -> Rn, functions Rn -> R, and vector fields Rn -> Rn), graphs, level sets of functions, examples. CM 12.2,3.

    Thu 01 Sep
    Vectors (position and displacement vectors), equations of lines (parametrization via point and vector) and planes (point and normal vector, three points) in Rn, dot product and cross product. CM 12.4, 13.1-4.

    Problem Set #1 due Fri 02 Sep
    Solutions #1

  3. Tue 06 Sep
    Parameterizing the intersection of two planes, tangent planes to special surfaces. CM 14.1-3.

    Thu 08 Sep
    Partial derivatives, gradients, tangent planes to graphes and to level surfaces, total derivative. CM 14.4-5.

    Problem Set #2 due Fri 9 Sep
    Solutions #2

  4. Tue 13 Sep
    More gradients, parameterized curves, velocity vector. CM 14.4-5, 17.1-2.

    Thu 15 Sep
    More parameterized curves, different parameterizations, velocity vector, chain rule for compositions of curves with functions. CM 17.1-2.

    Problem Set #3 due Fri 16 Sep
    Solutions #3

    Midterm #1 Practice Exam
    Midterm #1 Practice Exam solution guide.

  5. Tue 20 Sep
    Quiz #1 (20 min in class) solutions
    Curves on graphs of functions, steepest ascents. CM 17.2-4.

    Thu 22 Sep
    Review of Quiz #1 and review for Midterm #1

    Problem Set #4 due Fri 23 Sep
    Solutions #4

  6. Tue 27 Sep
    Midterm #1 (1 hour 10 min in class)
    Thu 29 Sep
    Visualizing vector fields, gradient fields, a vector field that is not a gradient field, Line integrals. CM 17.3-4, CM 18.1-3.

  7. Tue 04 Oct
    More vector fields, equipotential curves, flow curves. CM 17.3-4.

    Field potentials webapp at Davidson College.
    Vector field demonstrations at Wolfram web resourceas.
    Electric field applet at CalTech

    Thu 06 Oct
    More line integrals, path-independance, line integrals around closed curves, fundamental theorem of calculus for line integrals. CM 18.1-3.

    Problem Set #5 due Fri 07 Oct

  8. Tue 11 Oct
    Fall break!

    Thu 13 Oct
    More line integrals, fundamental theorem of calculus for line integrals, path-independant/conservative/gradient vector fields all the same, scalar curl test. CM 18.1-4.

    Problem Set #6 due Fri 14 Oct

  9. Tue 18 Oct
    More scalar curl, regions of definition, simply connected regions in the plane. Intro to multi-dimensional integrals. CM 18.1-4, 16.1.

    Thu 20 Oct
    Multi-dimensional integrals, iterated integrals, Fubini's theorem, integrating over boxes, triangles. CM 16.1-2.

    Problem Set #7 due Fri 21 Oct

  10. Tue 25 Oct
    Quiz #2 (20 min in class)
    More multi-dimensional integrals, iterated integrals over non-boxes, order of integration. CM 16.1-2.

    Thu 27 Oct
    Quiz #2 review, more multi-dimensional integrals, polar coordinates triple integrals, polar coordinates, cyclindrical coordinates. CM 18.4, 16.3-4

    Problem Set #8 due Fri 28 Oct

    Midterm #2 Practice Exam
    Midterm #2 Practice Exam solution guide.

  11. Tue 01 Nov
    More multi-dimensional integrals, more polar coordinates, more triple integrals, cyclindrical coordinates. CM 16.5.

    Thu 03 Nov
    More multi-dimensional integrals, more triple integrals, cyclindrical coordinates, solids of rotation. CM 16.5.

    Problem Set #9 due Fri 04 Nov

  12. Tue 08 Nov
    Midterm review!
    Thu 10 Nov
    Midterm #2 (1 hour 10 min in class)

  13. Tue 15 Nov
    Spherical coordinates, general change of variables formula. CM 16.5-7.

    Thu 17 Nov
    General change of coordinate formula. CM 16.7.

    Problem Set #10 due Fri 18 Nov

  14. Tue 22 Nov
    New York Times problem, change of variables variations.

    Thu 24 Nov
    Thanksgiving!

  15. Tue 29 Nov
    Parameterized surfaces, flux integrals. CM 19.1-3.

    Thu 01 Dec
    More flux integrals. CM 17.5, 19.1-3.

    Problem Set #11 due Fri 02 Dec

  16. Tue 06 Dec
    Last day of classes!

  17. Tue 13 Dec
    Final review session, Tue 13 Dec, 9-11 am, MSC E408.

    Final Study Guide and Practice Exam
    Solution guide!


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